Decomposition and interpretation of Gini and the generalized entropy inequality measures

The main purpose of this research is to deduce and analyse a new decomposition of the Gini index, and to present and analyse a decomposition of the generalized entropy inequality measure, deducing from the latter the particular cases corresponding to Theil, Hirschman-Herfindahl, and Bourguignon indexes. While the generalized entropy index is decomposed into its two conventional components of the inequality within and between subpopulations, the Gini index is decomposed into the following three components: (I) the Gini index within subpopulations; (II) the Gini index between subpopulations; and (III) the income transvariation between subpopulations. The Gini, Theil, Hirschman-Herfindahl and Bourguignon inequalities are applied to the 1995 italian family income distribution disaggregated by territorial area.